(like a tensor) · From eq. (2.26), the third of eqs. (2.27), and the second of eqs. (2.31), we can...

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Transcript of (like a tensor) · From eq. (2.26), the third of eqs. (2.27), and the second of eqs. (2.31), we can...

Page 1: (like a tensor) · From eq. (2.26), the third of eqs. (2.27), and the second of eqs. (2.31), we can visualize a x b as a vector normal to the plane defined by a and b; the length
Page 2: (like a tensor) · From eq. (2.26), the third of eqs. (2.27), and the second of eqs. (2.31), we can visualize a x b as a vector normal to the plane defined by a and b; the length

(nn)

[nn]

Page 3: (like a tensor) · From eq. (2.26), the third of eqs. (2.27), and the second of eqs. (2.31), we can visualize a x b as a vector normal to the plane defined by a and b; the length

(like a tensor)

Page 4: (like a tensor) · From eq. (2.26), the third of eqs. (2.27), and the second of eqs. (2.31), we can visualize a x b as a vector normal to the plane defined by a and b; the length

This is the reasonfor doing cofactors.

Page 5: (like a tensor) · From eq. (2.26), the third of eqs. (2.27), and the second of eqs. (2.31), we can visualize a x b as a vector normal to the plane defined by a and b; the length

useful special cases

cross product

Page 6: (like a tensor) · From eq. (2.26), the third of eqs. (2.27), and the second of eqs. (2.31), we can visualize a x b as a vector normal to the plane defined by a and b; the length
Page 7: (like a tensor) · From eq. (2.26), the third of eqs. (2.27), and the second of eqs. (2.31), we can visualize a x b as a vector normal to the plane defined by a and b; the length

cross productwith matrices:handy to have fornon-GA people

for future reference...

ax

Page 8: (like a tensor) · From eq. (2.26), the third of eqs. (2.27), and the second of eqs. (2.31), we can visualize a x b as a vector normal to the plane defined by a and b; the length

projection on (dual) plane n

Page 9: (like a tensor) · From eq. (2.26), the third of eqs. (2.27), and the second of eqs. (2.31), we can visualize a x b as a vector normal to the plane defined by a and b; the length
Page 10: (like a tensor) · From eq. (2.26), the third of eqs. (2.27), and the second of eqs. (2.31), we can visualize a x b as a vector normal to the plane defined by a and b; the length

Rodrigues: R = I cosQ + (1-cosQ ) nnT + sinQ nx

= I + sinQ nx + (1-cosQ) (nx)2